THE EQUILIBRIUM OF ELASTIC SOLIDS. 53 



the change of internal capacity depends entirely on the cubical elasticity of the 

 vessel, and not on its thickness or linear elasticity. 



When the external and internal pressures are inversely as the cubes of the 

 radii of the surfaces on which they act, 



a 3 , . a ' 



f mt li"u *l~ ~ 2 r "i 



SF _ a, 3 A t , , 



~T~' ~%^m 



= -t- 1 



In this case the change of capacity depends on the linear elasticity alone. 



M. Regnault, in his researches on the theory of the steam engine, has 

 given an account of the experiments which he made in / order to determine 

 with accuracy the compressibility of mercury. 



He considers the mathematical formulas very uncertain, because the theories 

 of molecular forces from which they are deduced are probably far from the 

 truth ; and even were the equations free from error, there would be much 

 uncertainty in the ordinary method by measuring the elongation of a rod of 

 the substance, for it is difficult to ensure that the material of the rod is the 

 same as that of the hollow sphere. 



He has, therefore, availed himself of the results of M. Lam4 for a hollow 

 sphere in three different cases, in the first of which the pressure acts on the 

 Ulterior and exterior surface at the same time, while in the other two cases 

 the pressure is applied to the exterior or interior surface alone. Equation (39) 

 becomes in these cases, 



5\ V 7i 



1. When &i = hj, -^ = and the compressibility of the enclosed liquid being 



H 1 



fa, and the apparent diminution of volume S'F, 



(42). 



* v-i 



2. When ^ = 0, 



} (43). 



2W 



